Example 29.43.2. Let S be a scheme. Let \mathcal{A} be a quasi-coherent graded \mathcal{O}_ S-algebra generated by \mathcal{A}_1 over \mathcal{A}_0. Assume furthermore that \mathcal{A}_1 is of finite type over \mathcal{O}_ S. Set X = \underline{\text{Proj}}_ S(\mathcal{A}). In this case X \to S is projective. Namely, the morphism associated to the graded \mathcal{O}_ S-algebra map
is a closed immersion, see Constructions, Lemma 27.18.5.
Comments (2)
Comment #8109 by Laurent Moret-Bailly on
Comment #8220 by Stacks Project on